Rocketship Education, the upstart charter operator that has posted impressive test scores for traditionally struggling students, won approval early Thursday morning to more than triple its charter network by opening 20 new schools in Santa Clara County — the largest single charter-school approval in the state.

After hearing parents desperately pleading for better schools and local school officials begging for more time, the Santa Clara County Board of Education voted to approve Rocketship’s petitions to open more K-5 schools in areas currently served by low-performing schools.

At the seven-hour meeting, a parade of high-profile Silicon Valley leaders joined purple-shirted Rocketship parents in asking the board to approve more charter schools, to help close the achievement gap.

But representatives of about a dozen local school districts argue that they, and not the county school board, should be the ones weighing the charter applications. “Districts are ready to work with charters and you are trying to stop that,” said Pam Parker, president of the Santa Clara County School Boards Association.

Rocketship’s 20 new countywide charter schools — to be phased in from 2013 to 2016 — would be located within the Alum Rock, Franklin-McKinley, Evergreen, Campbell elementary, Oak Grove, Mount Pleasant, San Jose Unified and Santa Clara Unified school districts.

The board voted 5-2 on most of Rocketship’s petitions, with trustees Anna Song and Michael Chang dissenting. Song chided Rocketship as untrustworthy, for claiming to be a school district in order to skirt local planning ordinances in building its schools, and for holding board meetings in places not easily accessible by the public. Chang said he preferred Rocketship to seek charters from local districts.

On two petitions for schools to be located within San Jose Unified, board President Joseph Di Salvo joined the dissenters.

The county board’s approval will bump up the number of children served by Rocketship Education to more than 14,000 students, a size equal to some of the largest school districts in Santa Clara County. Already, Rocketship runs five charter schools in San Jose, with three or four more slated to open in August.

Rocketship maintains that it is responding to tremendous demand from parents currently poorly served by local school districts. In Santa Clara County, 97 schools serving 40,000 students perform below the state’s goal of 800 on the 200-to-999 point Academic Performance Index.

As in past meetings, Rocketship bused in parents and children to attend, with many waving signs of support. “Thousands are depending on your courageous vote,” read one. “Their future depends on it.”

Parents spoke about how their children’s academic performance suffered at local district schools. “I am very sad to see the low level of education my children got,” said Maria Gomez, a resident of the Mount Pleasant School District. Her fourth-grade son transferred to Rocketship Discovery Prep just this year, and in three months, he’s already gained more than a year in reading levels, she said.

“Our students do not have time for the public education system to improve,” said another Discovery Prep parent, Donna Ikebe.

In contrast, Leslie Reynolds, a San Jose Unified trustee, said, “We are not clear what the big rush is.” She and other trustees of local school districts forcefully opposed the petitions, in part for bypassing their boards and going directly to the county board.

Rocketship officials have argued that running schools chartered by local districts, rather than by the County Office of Education, could shut out some targeted students: low-income, low-performing students throughout the county. Under a district charter, resident students — regardless of family income — have priority over students residing in other districts.

In the end, the board heeded parents’ pleas. “We are at a crossroads here, and we have a chance to take the road that will change everything,” said trustee Julia Hover-Smoot. “I cannot in good conscience ask parents to wait.”